Analysis of a One-Dimensional Model for Compressible Miscible Displacement in Porous Media
Youcef Amirat, Mohand Moussaoui · SIAM Journal on Mathematical Analysis · 1995
We consider a one-dimensional model problem for the motion of compressible miscible fluids in porous media, without molecular diffusion or dispersion, governed by a nonlinear hyperbolic-parabolic system. We assume the viscosity to be constant. We establish an existence result for nonsmooth data for the concentration. In the case of Dirichlet boundary conditions for the pressure, assuming the data to be smooth, we prove the existence and uniqueness of a smooth solution.